5a^2-13ab+6b^2=0

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Solution for 5a^2-13ab+6b^2=0 equation: 


Simplifying
5a2 + -13ab + 6b2 = 0

Reorder the terms:
-13ab + 5a2 + 6b2 = 0

Solving
-13ab + 5a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -2b)(5a + -3b) = 0


Subproblem 1
Set the factor '(a + -2b)' equal to zero and attempt to solve:

Simplifying
a + -2b = 0

Solving
a + -2b = 0

Move all terms containing a to the left, all other terms to the right.

Add '2b' to each side of the equation.
a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
a + 0 = 0 + 2b
a = 0 + 2b
Remove the zero:
a = 2b

Simplifying
a = 2b

Subproblem 2
Set the factor '(5a + -3b)' equal to zero and attempt to solve:

Simplifying
5a + -3b = 0

Solving
5a + -3b = 0

Move all terms containing a to the left, all other terms to the right.

Add '3b' to each side of the equation.
5a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
5a + 0 = 0 + 3b
5a = 0 + 3b
Remove the zero:
5a = 3b

Divide each side by '5'.
a = 0.6b

Simplifying
a = 0.6b
Solution
a = {2b, 0.6b}

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